52 



can be deduced. For normal midship sections, the relations between resistance 

 R and >S are similar to the corresponding ones between resistance and draft. Un- 

 fortunately, no numerical results of calculations are available at present and 

 no experiments are known which correspond closely to this problem; therefore, 

 we must confine ourselves to qualitative estimates which will be replaced by 

 more adequate data as soon as the pertaining calculations are completed. 



In the region of the first hump, the exponent p in Equation [21] is 

 nearer to 2 than to one; hence, small midship coefficients are used in actual 

 design. In the neighborhood of the second hump, high values are common; 

 this is reasonable although the Influence of the midship coefficient on resist- 

 ance is not negligible, since the use of a large ff value admits of the choice 

 of low prismatics without reducing unduly the block coefficient 6. 



D.W. Taylor's famous experiments dealing with the resistance R as a 

 function of the midship-section shape*^ refer to a rather complicated case. 

 They prove, however, that for high Froude numbers the influence of the ratios 

 B/L, H/L and /? upon R is similar; for moderate and low F-values, the effect 

 of the ratio B/L becomes predominant. More definite information will follow 

 from the systematic resistance evaluations mentioned earlier. 



When the shape of the midship section departs from the normal, spec- 

 ial investigations become necessary. These can be performed comparatively 

 easily, however. 



In many cases a rule of thumb method proves useful: By shifting 

 some of the submerged volume near the surface vertically downwards the resist- 

 ance is decreased. The effectiveness of such a change increases with the ra- 

 tio of the distance d by which the volume is moved to the length of the free 

 wave. 



d 



X " 27rF''L 

 i.e., decreases with Increasing Froude numbers. 



[28] 



3 .4.2 Shape of Sections, Load Water Line and Sectional- Area Curve 



Let the sectional area curve A (^) be given. 



The problem of developing good sections can then be replaced to some 

 extent by the simpler one of developing a suitable load water line X(|), at 

 least from the point of view of minimum wave resistance . 



Within the range of validity of the present theory it can be 

 inferred that reasonable changes in the shape of the sections have only a 

 secondary influence on the wave resistance once the A (^) and X(^) are fixed. 



